Properties of Polygons



Parallelograms





180(n-2) = SUM
o
n = # of sides of the polygon
o
SUM = sum of all the interior angles of the polygon
The sum of all exterior angles of a polygon is 360°
Regular polygons have sides and angles that are all congruent
# of Sides:
Name:
7
Heptagon
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
Both pairs of opposite angles are congruent
All adjacent angles are supplementary
Diagonals bisect each other
A Quadrilateral is a Parallelogram if…


Any of the above are true
One pair of opposite sides are both congruent and parallel
Rhombuses
Rectangles


Have all the properties of parallelograms,
plus…
o
All sides are congruent
o
Diagonals are perpendicular
o
Diagonals are angle bisectors
Have all the properties of parallelograms,
plus…
o
All angles are congruent (90°)
o
Diagonals are congruent
Squares

Have all the properties of parallelograms, rhombuses and rectangles
o
A square IS a parallelogram, rhombus and rectangle
Summary
Trapezoids
If a statement is ALWAYS true for a type of quadrilateral, then there is an X in the box.





Are NOT parallelograms
Exactly one pair of opposites sides is parallel
The parallel sides are called bases
The non-parallel sides are called legs
MIDSEGMENT: The midsegment of a trapezoid is
a segment that connects the midpoints of the legs
Isosceles Trapezoids

Have all the properties of trapezoids, plus…
o
Base angle pairs are congruent
o
Legs are congruent (but bases are
NEVER congruent in a trapezoid)
o
Diagonals are congruent
Kites





Are NOT parallelograms
Opposite sides are NOT congruent
Two pairs of adjacent sides ARE congruent
Diagonals are perpendicular
Exactly one pair of opposite angles are congruent
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
#
1
2
3
4
5
6
7
8
9
10
11
12
13
All sides are congruent
Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
All angles are congruent
Exactly one pair of opposite sides are congruent
Exactly one pair of opposite angles are congruent
Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect each other
Exactly one pair of opposite sides are parallel
Two pairs of adjacent sides are congruent
Diagonals are angle bisectors
All adjacent angles are supplementary
Quad.
II-gram
X
X
Rhomb.
X
X
X
Rect.
X
X
X
Square
X
X
X
X
Trap.
Is. Trap.
Kite
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Practice Worksheet: You can print this page multiple times for practice. If you do this correctly, you know this topic very well!
If a statement is ALWAYS true for a type of quadrilateral, then write an X in the box.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
#
1
2
3
4
5
6
7
8
9
10
11
12
13
All sides are congruent
Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
All angles are congruent
Exactly one pair of opposite sides are congruent
Exactly one pair of opposite angles are congruent
Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect each other
Exactly one pair of opposite sides are parallel
Two pairs of adjacent sides are congruent
Diagonals are angle bisectors
All adjacent angles are supplementary
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square
Trapezoid
Isosceles Trapezoid
Kite